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The central vertices and radius of the regular graph of ideals | ||
| Transactions on Combinatorics | ||
| مقاله 1، دوره 6، شماره 4، اسفند 2017، صفحه 1-13 اصل مقاله (246.63 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2017.21472 | ||
| نویسنده | ||
| Farzad Shaveisi* | ||
| Razi University | ||
| چکیده | ||
| The regular graph of ideals of the commutative ring $R$, denoted by ${\Gamma_{reg}}(R)$, is a graph whose vertex set is the set of all non-trivial ideals of $R$ and two distinct vertices $I$ and $J$ are adjacent if and only if either $I$ contains a $J$-regular element or $J$ contains an $I$-regular element. In this paper, it is proved that the radius of $\Gamma_{reg}(R)$ equals $3$. The central vertices of $\Gamma_{reg}(R)$ are determined, too. | ||
| کلیدواژهها | ||
| Arc؛ artinian ring؛ eccentricity؛ radius؛ regular digraph | ||
| مراجع | ||
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[6] H. R. Dorbidi and R. Manaviyat, Some results on the comaximal ideal graph of a commutative ring, Trans. Comb., 5 no. 4 (2016) 9-20.
[7] M. J. Nikmehr and F. Shaveisi, The regular digraph of ideals of a commutative ring, Acta Math. Hungar., 134 (2012) 516-528.
[8] F. Shaveisi, Some results on the annihilating-ideal graphs, Canad. Math. Bul l., 59 no. 3 (2016) 641-651.
[9] F. Shaveisi and R. Nikandish, The nil-graph of ideals of a commutative ring, Bul l. Malays. Math. Sci. Soc. (2), 39 no. 1 (2016) 3{11.
[10] T. Tamizh Chelvman and S. Nithya, A note on the zero divisor graph of a latice, Trans. Comb., 3 no. 3 (2014) 51-59. | ||
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